{"id":241688,"date":"2025-07-03T19:52:11","date_gmt":"2025-07-03T19:52:11","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=241688"},"modified":"2025-07-03T19:52:13","modified_gmt":"2025-07-03T19:52:13","slug":"complete-the-following-statement-of-congruence-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/03\/complete-the-following-statement-of-congruence-2\/","title":{"rendered":"Complete the following statement of congruence"},"content":{"rendered":"\n
Complete the following statement of congruence<\/pre>\n\n\n\n
\"\"<\/figure>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
The correct answer is B. \u0394ACB<\/strong>.<\/p>\n\n\n\n
Explanation<\/h3>\n\n\n\n
To complete the statement of congruence, \u0394XZY \u2245 _____, we must identify the corresponding vertices of the two triangles in the correct order. Congruent triangles have identical corresponding sides and angles. The order of the vertices in a congruence statement indicates which parts correspond to each other.<\/p>\n\n\n\n
Let’s analyze the two triangles, \u0394XZY and \u0394ABC, to find the matching vertices.<\/p>\n\n\n\n
    \n
  1. Identify Corresponding Angles:<\/strong>\n
      \n
    • First, we can observe the right angles. In \u0394XZY, the right angle is at vertex\u00a0X<\/strong>. In the other triangle, the right angle is at vertex\u00a0A<\/strong>. Therefore, vertex X corresponds to vertex A.<\/li>\n\n\n\n
    • Next, let’s look at the other vertices based on their positions. Vertex\u00a0Z<\/strong>\u00a0is at the top of the vertical side of \u0394XZY. In the second triangle, vertex\u00a0C<\/strong>\u00a0is in the equivalent position, at the top of its vertical side. This means vertex Z corresponds to vertex C.<\/li>\n\n\n\n
    • Finally, vertex\u00a0Y<\/strong>\u00a0is at the end of the horizontal side, opposite the vertical side. In the second triangle, vertex\u00a0B<\/strong>\u00a0is in the same relative position. Thus, vertex Y corresponds to vertex B.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • Construct the Congruence Statement:<\/strong>
      The problem asks for a triangle congruent to \u0394XZY. We must list the corresponding vertices of the second triangle in the same sequence as X, Z, and Y.
      • The first vertex,\u00a0X<\/strong>, corresponds to\u00a0A<\/strong>.<\/li>
      • The second vertex,\u00a0Z<\/strong>, corresponds to\u00a0C<\/strong>.<\/li>
      • The third vertex,\u00a0Y<\/strong>, corresponds to\u00a0B<\/strong>.<\/li><\/ul>By putting these corresponding vertices together in the correct order, we get the triangle\u00a0\u0394ACB<\/strong>.<\/li>\n<\/ol>\n\n\n\n
        Therefore, the complete and correct statement of congruence is\u00a0\u0394XZY \u2245 \u0394ACB<\/strong>. This statement correctly implies that all corresponding parts are congruent: \u2220X \u2245 \u2220A, \u2220Z \u2245 \u2220C, \u2220Y \u2245 \u2220B, and side XZ \u2245 side AC, side ZY \u2245 side CB, and side YX \u2245 side BA. Option B is the only choice that reflects this proper correspondence<\/p>\n\n\n\n
        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"
        Complete the following statement of congruence The Correct Answer and Explanation is: The correct answer is B. \u0394ACB. Explanation To complete the statement of congruence, \u0394XZY \u2245 _____, we must identify the corresponding vertices of the two triangles in the correct order. Congruent triangles have identical corresponding sides and angles. The order of the vertices in […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-241688","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/241688","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=241688"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/241688\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=241688"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=241688"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=241688"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}